Prove that the set of points (p,q) on the plane - (where p,q are rational coordinates) is countable. I don't understand what I need to do to prove this
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The problem asks you to show that the set $\{\langle p,q\rangle\in\Bbb R^2\mid p,q\in\Bbb Q\}=\Bbb{Q\times Q}$ is countable.
To prove this, recall that $\Bbb Q$ is countable, and use the basic theorems about countable sets.
Asaf Karagila
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Dear Asaf - Moments ago came the message that moderator elections are upon us. If it's something you would consider, I would be delighted to nominate you - as I am sure many others would as well. Regrads, – Dec 08 '14 at 20:11
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@Andrew: Thanks for the support. I am not personally cut for being a moderator on this website. I have declared that more than several times already that I will never, ever ever consider taking moderatorship on this website. But thanks for the vote of confidence. – Asaf Karagila Dec 08 '14 at 20:13